The invention is based on a process for operating an internal combustion engine and a fuel injection system for carrying out the process. A process of this kind is realized with known fuel injection systems which provide the fuel to be injected in a high pressure fuel reservoir. However, due to the continuously available fuel under high pressure, this brings about the danger that in the event of a failure of the fuel injection valve or its electrical control, the fuel injection valve remains in the open position after a fuel injection so that furthermore, fuel under high pressure is continuously fed into the respective combustion chamber of the engine. This fuel quantity can be abruptly ignited together with the fresh air that is brought in again in the subsequent compression stroke. This leads to a considerable generation of heat connected with an extreme pressure increase, which is not provided for in the normal operation of the engine and consequently can lead to the destruction of the engine.